200 DOC.
17
PROBLEM
OF
GRAVITATION
[8]
(generalized
Lorentz
transformations),
4.
The observable laws
of
nature
do
not
depend on
the absolute
magnitude
of
the
gravitational potential (or
gravitational
potentials). Physically,
this
means
the
following:
The
set
of relations between observable
quantities
that
one can
determine in
a laboratory
is not
changed
if
I
bring
the whole
laboratory
into
a
region
of
a
different
(spatially
and
temporally
constant)
gravitational
[9]
potential.
The
following
should
be noted
regarding
these
postulates.
All
theoreticians
will
agree
with
one
another that
postulate
1
must be
adhered
to.
There will be
no
such
[10]
general
consensus
regarding
adherence
to
postulate
3.
Thus,
M.
Abraham has
propounded
a
theory
of
gravitation
that does
not
satisfy postulate
3. I could subscribe
to
this
standpoint
if,
in
Abraham's
system,
there
were
covariance with
respect
to
transformations that
turn
into linear
orthogonal
transformations in
regions
of constant
gravitational potential;
but this does
not
seem
to
be the
case
with Abraham's
theory.
Thus,
his
theory
does not contain
as a special case
the
theory
of
relativity
in the form
in which it has
developed
so
far,
exclusive of
gravitation.
All of those
arguments
that
have been
put
forward
for
the
theory
of
relativity
in its
present
form
speak against
such
a
theory.
In
my opinion
it
is
absolutely necessary
to
stick with
postulate 3
as
long
as
there
are no
compelling reasons
for not
doing so;
the
moment
we
abandon
this
postulate,
the manifold
of
possibilities
will become indeterminable.
A
more
careful examination is
required
for
postulate 2,
which,
in
my opinion,
we
must
hold
on
to
unconditionally
until the
contrary
has been
proved.
The
postulate
is
based first
of
all
on
the
empirical
fact that all bodies in
a
gravitational
field fall with
the
same
acceleration;
we
will
once again
have
to
pay
attention
to
this
important
point
later
on.
Let
it
only
be noted here that the
equality
(proportionality)
of
the
gravitational
and inertial
mass
has been
proved
with
great accuracy
in
an
investiga-
tion
of
great
importance
to
us
by Eötvös;1
he
proved
this
proportionality by
demonstrating experimentally
that
the resultant of
gravitation
and the
centrifugal
force
produced by
the rotation of Earth is
independent
of the nature
of
the material
(the
relative difference between
the
two
masses 10-7).
Taken
together
with
one
of
the
main results
of
the
ordinary
theory
of
relativity, postulate
2 leads
to
a
conclusion that
shall be drawn
already
at this
point. According
to
the
theory
of
relativity,
the inertial
mass
of
a
closed
system
(the
latter
being
considered
as a
whole)
is determined
by
its
[12]
energy.
According
to
2,
the
same
must
also hold
true
for the
gravitational
mass.
Thus,
if
the state of
a
system
changes
in
an arbitrary
fashion but without
its
total
energy being changed,
then the distant
gravitational
action of the
system
does
not
change,
not
even
if
a
part
of
the
energy
of the
system
is
converted into
gravitational
[11] 1B. Eötvös,
Mathem.
und
naturw.
Ber.
aus Ungarn 8
(1890).
Beibl.
15 (1891):
688.